So it was a float switch cutting off the condensor? Duh shoulda thought of that.
Cleaning the coil on the inside I would be careful using a hose might get alot of water in your attic,closet..wherever your furnace and coil is, or air handler or whatever tons of Air Conditioning units. they make an Aerosal Can of coil clean that works pretty damn well for not needing to rinse it off. Just go to home depot find the can, dooesnt matter which brand . We use whichever is on sale at the time

Inbetween the furnace and the coil should be a metal transition or duct board. cut a hole in it large enough to peel back and fit the can inside. and spray the entire surface down. then turn the unit back on and when it starts creating condensation it will rinse it for you. Can also use a metal brush to get the huge gunk off. On the outside use the hose dont spray tooo hard though or you can bend the fins and that can both make it harder to "breathe" and  could straight up  puncture it. Sounds like ya got off pretty good though.

Oh also in the main drain from your coil if it doesnt have a Tee in the drain so you can pour bleach into it once a month. Add one. Simple cheap pvc from home depot again and then if you once a month pour bleach in your drain, you wont ever have build up.

no more then 100 thats with the upsale they have to make above cost. good price will be 80. and the big big companies could be as high as 250(dont ever play with those guys , outrageous prices. Plus the service call, ours down here is 39.95 , but some of the big boys charge as high as 70 for a service call! thats crazy! heh.
Id pay the service call and see what he says. if you feel it to be outrageous. call someone else cause it prolly is.

Judging by you saying it never meets the desired temperature. You prolly have a dirty coil(can do that yourself with minimal labor with an aerosol can from home depot).
Could be your ductwork also, but usually not that. Could be low on freon between that and a capacitor thats the usual suspect. However thats bad cause if its low, you have a leak in the coil or condensor. Anyway Ill be around today its in the 70's so I Dont work when people arent hot or cold

yup, turn it off. spin the blade if it spins prolly just a capacitor. prolly that anyway replaced a good 200 this summer on top of real issues . btw if it isnt blowing turn it off so it doesnt freeze and flood your house with water

thanks for the warm welcome@! bring some more pvp to LA! i wanna try out these faction items!